# Thermal energy problem: Gas expansion in cylinder

• Bonapartist
In summary, the problem involves a vertical heat-insulated cylinder divided by a movable piston, with the top part being evacuated and the bottom part filled with 1 mol of monatomic gas at 300 K. After the piston is released and equilibrium is reached, the volume of the gas is halved and the final temperature of the gas is found using the adiabatic process equation PVk=const. The final temperature is calculated to be 476.22 K.
Bonapartist

## Homework Statement

A vertical heat-insulated cylinder is divided into two parts by a movable piston of mass m. Initially, the piston is held at rest. The top part is evacuated and the bottom part is filled with 1 mol of monatomic gas at temperature 300 K. After the piston is released and the system comes to equilibrium, the volume occupied by the gas is halved. Find the final temperature of the gas.

PV = nRT
S = Q/T
mg = PA?[/B]

## The Attempt at a Solution

I've attempted to solve this problem using the fact that mg = PA and that the pressure can be solved for. Is this incorrect?

Thanks! As the first time I've posted on PF, I am delighted to be a contributing member!

Bonapartist said:

## Homework Statement

A vertical heat-insulated cylinder is divided into two parts by a movable piston of mass m. Initially, the piston is held at rest. The top part is evacuated and the bottom part is filled with 1 mol of monatomic gas at temperature 300 K. After the piston is released and the system comes to equilibrium, the volume occupied by the gas is halved. Find the final temperature of the gas.

PV = nRT
S = Q/T
mg = PA?[/B]

## The Attempt at a Solution

I've attempted to solve this problem using the fact that mg = PA and that the pressure can be solved for. Is this incorrect?

Thanks! As the first time I've posted on PF, I am delighted to be a contributing member!
Considering the process is adiabatic(ideally insulated q=0, no heat transfer involved in the process), use PVk=const or P1V1k=P2V2k
k is just the heat capacity ratio of the gas given k=Cp/Cv

Bonapartist
I've solved it to be 476.22 K, a reasonable answer. Thanks for pointing out its adiabatic nature!

Bonapartist said:
I've solved it to be 476.22 K, a reasonable answer. Thanks for pointing out its adiabatic nature!

## 1. What is thermal energy and how does it relate to gas expansion in a cylinder?

Thermal energy is a form of energy that is associated with the motion of atoms and molecules. In the case of gas expansion in a cylinder, thermal energy is responsible for the movement of gas molecules, causing them to expand and exert pressure on the walls of the cylinder.

## 2. What factors affect the amount of thermal energy produced during gas expansion in a cylinder?

The amount of thermal energy produced during gas expansion in a cylinder depends on the initial temperature and pressure of the gas, the volume of the cylinder, and the type of gas. Additionally, the speed of the expansion and the presence of any external heat sources or sinks can also affect the amount of thermal energy produced.

## 3. How does the ideal gas law relate to thermal energy in a gas expansion problem?

The ideal gas law, PV = nRT, describes the relationship between pressure, volume, temperature, and the number of moles of gas in a system. In a gas expansion problem, the ideal gas law can be used to calculate the change in thermal energy by solving for the change in temperature (ΔT) using the equation ΔT = (PΔV)/nR.

## 4. What is the significance of heat transfer in a thermal energy problem involving gas expansion in a cylinder?

Heat transfer refers to the transfer of thermal energy from one object or system to another. In a gas expansion problem, heat transfer can occur through conduction, convection, or radiation, and it can affect the overall thermal energy of the system. Additionally, heat transfer can also be used to control the temperature and pressure of the gas during expansion.

## 5. How can the first law of thermodynamics be applied to a thermal energy problem involving gas expansion in a cylinder?

The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or converted from one form to another. In a gas expansion problem, the first law of thermodynamics can be applied to calculate the change in internal energy (ΔU) by considering the work done by the gas (W) and the heat transfer (Q) into or out of the system, using the equation ΔU = Q - W.

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